Question

Find the indicated limit, if it exists.

limit of f of x as x approaches 0 where f of x equals 10 x plus 2 when x is less than 0 and the absolute value of the quantity 2 minus x when x is greater than or equal to 0

Answer 1

@Compassionate

Answer 2

@MrNood

Answer 3

draw

Answer 4

how? @Mateaus my lesson didnt show me how to do that

Answer 5

i can't read all that mess but i bet it is a piecewise function right?

Answer 6

no its limits, determining if its continuous

Answer 7

\[f(x) = \left\{\begin{array}{rcc}
10x + 2 & \text{if} & x <0 \\
2-x& \text{if} & x\geq 0
\end{array}
\right.\]

Answer 8

there does that look right?

Answer 9

yes!
the limit is x->2

Answer 10

as x goes to 2 or as x goes to zero?

Answer 11

oops i mean x->0

Answer 12

how'd i guess?

Answer 13

And the second has absolute value bars around it

Answer 14

this is really really much easier than it looks
replace \(x\) by \(0\) in both expressions
if you get the same number, that is the limit
if you get different numbers then there is no limit

Answer 15

Really? okay, ill try on some scratch paper,

Answer 16

do it in your head

Answer 17

what is \(10x+2\) if \(x\) is zero?

Answer 18

so they are continuos

Answer 19

its 2

Answer 20

nd the other is also 2

Answer 21

yes since if \(x=0\) you get \(2\) for both

Answer 22

so the limit is 2, correct?

Answer 23

So what about a problem with 2 instead of 0, the same would hold true? and if the values are not equal to the same thing, the limit does not exist?